Algebra 1 Common Core Student Edition, Grade 8-9

Think
H o w is th is in e q u a lity
different from others
you have seen before?
The expression f + 6
involves addition, so you
have to use subtraction
to undo the addition and
isolate the variable.

How do you know
which inequality
symbol to use?
W ords and phrases like
a t m ost, n o m o re th a n ,
and maximum may
indicate th a t you should
use s.

The Subtraction P roperty of Inequality is show n below.

Words

Key Concept Subtraction Property of Inequality

Diagram

Let a, b, and c b e r e a l n u m b e r s.

If a > b, then a - c> b - c.

If a<b, then a - c < b - c.

This p roperty is also tru e for > an d

Examples

—3 < 5, so —3 — 2 < 5 — 2.

3 > - 4 , so 3 - 1 > - 4 - 1.

The diagram below illustrates one way to

th in k ab o u t this rule.

-c

a - c

Using the Subtraction Property of Inequality

What are the solutions of t + 6 > — 4? Graph the solutions.

t+ 6 > - 4

t+ 6 ” 6 > -4 -6 Subtract 6 from each side,

t > —10 Simplify.

‘ ©.......I I1- "I I I * The solutions of f > -10 are all real numbers to the

-1 0 -8 -6 -4 -2 0 right of-10.

G o t It? 3. W hat are the solutions of - 1 ^ y + 12? G raph th e solutions.

Writing and Solving an Inequality

Computers The hard drive on your computer has a capacity of 120 gigabytes (GB).

You have used 85 GB. You want to save some home videos to your hard drive. What

are the possible sizes of the home video collection you can save?

Define Let v = the size of the video collection.

Write 85 + v < 120

85 + v < 120

85 + v — 85 ^ 120 - 85 Subtract 85 fro m each side,

n < 35 Simplify.

The h o m e video collection can be any size less th a n or equal to 35 GB.

size oi videos c ^is at m ost^ hard drive

capacity

c

Po w erAlg eb ra.com

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Lesso n 3-2 Solving Ineq ualit ies Using Ad d it ion or Subt ract ion 173